An unstable pathway to room temperature superconductivity?

In PNAS, an international collaboration among groups at the University of Houston and Rice University in the United States and Jilin and Linyi Universities in China reports a discovery that in iron-selenide (FeSe) superconductivity survives up to the four times higher temperature if the sample is pressure quenched (1). In what follows, I will try to explain why (I believe) this is very exciting and eye opening.

Kamerlingh Onnes, in 1911, observed that the electric resistivity of mercury vanished below T_c = 4.2 K. Subsequently, many other materials were also found to show superconductivity, but for well over six decades, this remained a very low–temperature phenomenon. Why this is so was explained by Bardeen, Cooper, and Schrieffer. Their (“BCS”) theory tied the maximal temperature at which superconductivity can survive in a particular material to its phonon and electron spectra and the electron–phonon interaction. The (simplest version of) BCS expression for that “critical” temperature (T_c) reads k_BT_c = 1.13ħω_D × exp[−1/N(0)V₀], where k_B and ħ are the Boltzmann and Planck constants, respectively; ω_D is the characteristic (Debye) phonon frequency; N(0) is the electronic density of states at the Fermi level; and V₀ is the electron–phonon coupling potential. Until the mideighties, if one inserted the parameters of any known superconducting material, one would infer that T_c < 25 K, in agreement with what was observed experimentally.

In principle, the BCS theory encodes a recipe of how to raise T_c: increase ω_D, N(0), and/or V₀. In practice, unfortunately, the parameters N(0) and V₀ are hard to change in a given material. One can increase ω_D, however, by applying a (high) pressure, and hence, this line of investigation has been ongoing since well over half a century ago. One of the pioneers has been Ching-Wu (Paul) Chu, who also led the study (1) we are commenting upon.

The quest for higher-T_c superconductors burgeoned in 1986 when superconductivity was discovered in a cuprate, La-Ba-Cu-O, with the onset at about 35 K. Within weeks, Paul Chu showed that T_c can be increased to over 50 K by applying a hydrostatic pressure of about 1 GPa (10,000 times higher than the atmospheric one) (2). A few months later, Chu and coworkers (3) discovered YBa₂Cu₃O₇ with T_c = 92 K. This was the first “liquid nitrogen” superconductor—meaning, with T_c > 77 K, the temperature of N₂ liquid at ambient pressure. The trick was to substitute La³⁺ with a smaller isovalent cation, Y³⁺, thus applying a very large “chemical pressure.” This discovery triggered a “high-T_c gold rush.” Within a couple years, a number of other cuprate superconductors were synthesized, with the highest T_c ∼ 133 K observed in HgBa₂Ca₂Cu₃O₁₀. Then, Chu struck again, raising this to 164 K under a large hydrostatic pressure of 45 GPa (4). This record stood unsurpassed for almost two decades.

In the meantime, theorists were busy exploring various conceivable strategies for raising T_c. An obvious one is to increase ω_D by choosing lighter atoms. Indeed, this points to hydrogen since it is the lightest of all elements; however, it solidifies only below 14 K, and it is insulating. Nevertheless, Wigner and Huntington (5) predicted long ago that hydrogen would turn metallic under pressure of 25 GPa. Ashcroft (6) raised the stakes further, arguing that if metallic hydrogen could be produced in this way, it would be a superconductor with T_c ∼ 200 K. However, subsequent estimates of the critical pressure [by Abrikosov, Ashcroft, Kagan, and coworkers (6–8)] were much higher than the original one by Wigner and Huntington (5)—as high as 1,500 GPa, which is way out of reach experimentally even today.

Naturally, this makes one turn to metallic hydrides and chemical pressure. My personal bet, since the seventies, has been on beryllium hydride polymer, (BeH₂)x. Today, it would be branded as a paradigmatic quantum material. It is an electron-deficient compound—meaning that it violates the textbook chemical valence rules and expectations. Its highest-occupied band is very flat, implying that if the material can be hole doped, N(0) would be quite high (9). It contains only the lightest atoms, so ω_D should also be very high. Last but not least, the topmost (flat) band is twofold degenerate throughout the Brillouin zone. This “band degeneracy” can only occur in quasione-dimensional materials and could give rise to an unusual phenomenon, a “band Jahn–Teller effect.” This is somewhat similar to the well-known Peierls’ transition, insofar that both originate from the vibronic (electron–phonon) coupling. However, there is also an important difference. In the Peierls’ transition, only a small fraction of electron states near the Fermi level is altered, and this results in a relatively weak logarithmic instability. In contrast, in (BeH₂)_x a structural distortion that breaks the fourfold rotation symmetry can make the twofold-degenerate band split off into two separate bands, so all the electrons are involved. This would result in a strong instability, linear in the atomic displacements, and hence, in very strong electron–phonon coupling. Thus, in (BeH₂)x we have all three ingredients for a very high T_c—high ω_D, N(0), and V₀—if only it can be made metallic.

Indeed, chemists have found a way to prepare crystalline (BeH₂)_x. Brendel et al. (10) mixed amorphous polymer (BeH₂)_x with some LiH, exposed this to a high temperature and pressure for a selected time interval, and then released both p and T. They explored the phase diagram up to about P = 1 GPa and T = 250 °C (during compaction/fusion) and discovered several crystalline phases, depending on p and T. The densest (0.77-g/cm³) phase was whitish in color and stable. However, if annealed within a certain narrow patch of the (p,T) space, a black and “metallic-like” phase formed. It was metastable, returning spontaneously back to the white insulating phase within few days. Regrettably, I could find very little about (BeH₂)_x in the open literature, other than (or perhaps because) it may be used as a solid rocket propellant, a very efficient neutron moderator, and a hydrogen storage material. As for other beryllium hydrides, Overhauser (11) conjectured in 1987 that LiBeH₃ and/or Li₂BeH₄ should have perovskite-like structures and show high-T_c superconductivity; however, neither compound turned out to be metallic. A decade later, a discovery of superconductivity at T_c > 350 in a powder composed of Li, Be, and H was announced (12) by a group in Lyon, France, but this result could not be reproduced, and the interest in Be-H compounds has subsided.

The hydride high-T_c revolution started for real in 2015, when Eremets and coworkers (13) reported superconductivity in sulfur hydride with T_c = 203 K, under the enormous pressure of about 100 GPa. This result has been confirmed by several other groups and extended to other hydrides, some with even higher T_c approaching room temperature. However, in all of these hydrides, superconductivity occurs only under extremely high pressures, and this hampers not just any applications but even the measurements of the key physical properties. To overcome that hurdle, a different line of attack was needed.

One has now been offered by Paul Chu (again) and his collaborators. The Rice team synthesized an FeSe sample, which under ambient pressure showed with T_c = 9.3 K. Then, using a special diamond-anvil cell, the Houston team subjected the sample to the pressure of about 45 GPa and found that T_c quadrupled. Next, keeping the sample at a low temperature (T = 4.2 K), they released the pressure relatively quickly (“pressure quenching”). Then, they remeasured the sample, under the normal ambient pressure, and found that upon warming up superconductivity persevered to about 37 K, about 400% the original T_c value. Notably, this enhanced superconductivity state is metastable, persisting for a week or more.

The idea can be conveyed by a metaphor, illustrated in Fig. 1. Imagine a ball in a vessel with two unequal minima, A and B. If we keep the vessel straight, the stable position of the ball is in the deeper minimum A. However, if we tilt the vessel enough, the other minimum will become lower. If the ball has enough kinetic energy to roll over the barrier, it will then go to the other well, and after some number of oscillations (damped by the friction), it will eventually stop at B. If we now until the vessel without shaking the ball much (so that its kinetic energy stays lower than the barrier), it will oscillate around B and eventually rest there. We have “frozen” the ball in a metastable state. What Deng et al. (1) have done is analogous—just replace my vessel’s shape with the Gibbs free energy (as a function of some atomic displacement coordinate), tilting by pressure, and kinetic energy by temperature. By pressure quenching at low temperature, Deng et al. (1) have frozen FeSe in a metastable phase.

Fig. 1.

Metastable state of a ball in a double-well dish. Tilting reduces the gravitational energy difference between the two minima, A and B. When the dish is tilted enough, the state B becomes more stable. Careful untilting leaves the ball in the state B, which is now metastable.

This in itself is hardly a miracle. Metastable states are ubiquitous wherever you look and on all scales. Metastable nuclei undergo radioactive decay. Metastable atoms are responsible for phosphorescence. We owe aurora borealis and aurora australis to radiation from metastable oxygen and nitrogen in the atmosphere. In the ruby laser, one first excites a short-lived high-energy state, which decays into a lower-energy state that is metastable and long lived; that is how Maiman achieved the population inversion and the stimulated emission. Sandpiles and snow slopes are metastable—hence, occasional avalanches. So are bowling pins—they are more stable when they tip over. Diamond lives forever (on our timescale) because of the huge kinetic barrier for its conversion to graphite, the thermodynamically stable form of carbon. Additionally, even the life as we know it involves metastability at various levels—that is why in our atmosphere trees do not spontaneously ignite and why the functional (folded) states of proteins do not decay into the more stable aggregated fibrillar states.

What is a great surprise and mystery, however, is that the metastable phase of FeSe discovered by Deng et al. (1) has four times higher T_c than the stable one. Most of us in the field do not believe that FeSe is in fact a BCS superconductor, and neither are other iron-chalcogenides nor iron-pnictides nor cuprates. However, we do not yet know what exactly makes them tick (i.e., there is no consensus on the theory of high-T_c superconductivity appropriate for these materials). Hence, for now we can only guess why this metastable FeSe phase is a better superconductor. In fact, at this point we do not even know what phase is; however, this probably will be sorted out before too long by structural, electronic, and other measurements and characterization. Then, perhaps we could turn the question upside down and from the fact that this metastable phase has a higher T_c, learn something vital about the underlying superconductivity mechanism.

What seems safe to predict is that this discovery will trigger much Edisonian, experimental search for new metastable superconductors since the recipe is relatively simple and straightforward—heat, compress, quench, dip. One can also use other and more broadly accessible ways of “tilting the potential,” like supercooling, kinetically controlled synthesis, epitaxial strain, electrolyte gating, photoexcitation, and pretty much any other way of reaching metastable states. Theorists could get busy as well, predicting deep metastable states and guiding the experiments. Perhaps a new high-T_c gold rush has just started.